000118881 001__ 118881
000118881 005__ 20250109150035.0
000118881 0247_ $$2doi$$a10.1016/j.jfa.2021.109291
000118881 0248_ $$2sideral$$a124982
000118881 037__ $$aART-2022-124982
000118881 041__ $$aeng
000118881 100__ $$0(orcid)0000-0003-1256-3671$$aAlonso Gutiérrez, David$$uUniversidad de Zaragoza
000118881 245__ $$aThin-shell concentration for random vectors in Orlicz balls via moderate deviations and Gibbs measures
000118881 260__ $$c2022
000118881 5060_ $$aAccess copy available to the general public$$fUnrestricted
000118881 5203_ $$aIn this paper, we study the asymptotic thin-shell width concentration for random vectors uniformly distributed in Orlicz balls. We provide both asymptotic upper and lower bounds on the probability of such a random vector $X_n$ being in a thin shell of radius $\sqrt{n}$ times the asymptotic value of $n^{-1/2}\left(\E\left[\Vert X_n\Vert_2^2\right]\right)^{1/2}$ (as $n\to\infty$), showing that in certain ranges our estimates are optimal. In particular, our estimates significantly improve upon the currently best known general Lee-Vempala bound when the deviation parameter $t=t_n$ goes down to zero as the dimension $n$ of the ambient space increases. We shall also determine in this work the precise asymptotic value of the isotropic constant for Orlicz balls. Our approach is based on moderate deviation principles and a connection between the uniform distribution on Orlicz balls and Gibbs measures at certain critical inverse temperatures with potentials given by Orlicz functions, an idea recently presented by Kabluchko and Prochno in [The maximum entropy principle and volumetric properties of Orlicz balls, J. Math. Anal. Appl. {\bf 495}(1) 2021, 1--19].
000118881 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E48-20R$$9info:eu-repo/grantAgreement/ES/MICINN PID2019-105979GB-I00
000118881 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
000118881 590__ $$a1.7$$b2022
000118881 591__ $$aMATHEMATICS$$b51 / 329 = 0.155$$c2022$$dQ1$$eT1
000118881 592__ $$a1.959$$b2022
000118881 593__ $$aAnalysis$$c2022$$dQ1
000118881 594__ $$a2.9$$b2022
000118881 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000118881 700__ $$aProchno, Joscha
000118881 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático
000118881 773__ $$g282, 1 (2022), 109291 [35 pp.]$$pJ. funct. anal.$$tJOURNAL OF FUNCTIONAL ANALYSIS$$x0022-1236
000118881 8564_ $$s1152950$$uhttps://zaguan.unizar.es/record/118881/files/texto_completo.pdf$$yPostprint
000118881 8564_ $$s1720532$$uhttps://zaguan.unizar.es/record/118881/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint
000118881 909CO $$ooai:zaguan.unizar.es:118881$$particulos$$pdriver
000118881 951__ $$a2025-01-09-14:59:00
000118881 980__ $$aARTICLE